Normalizing unbiased estimating functions

We consider a method for setting second-order accurate confidence intervals for a scalar parameter by applying normalizing transformations to unbiased estimating functions. Normalizing a nonlinear estimating function is usually easier than normalizing the estimator defined as the solution to the corresponding estimating equation. This estimator usually has to be obtained by some iterative algorithm. Numerical examples include a canonical Poisson regression and the estimation of the correlation coefficient. Numerical comparisons are made with the asymptotically equivalent method called estimating function bootstrap proposed recently by Hu and Kalbfleisch (Canad. J. Statist. 28 (2000) 449).